Linear programs with an additional separable concave constraint

Linear programs with an additional separable concave constraint

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Article ID: iaor20051121
Country: United States
Volume: 8
Issue: 3
Start Page Number: 155
End Page Number: 174
Publication Date: Oct 2004
Journal: Journal of Applied Mathematics & Decision Sciences
Authors: ,
Keywords: programming: branch and bound, programming: convex
Abstract:

In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk–Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we solve the problem alternating local search and branch-and-bound. In the indirect application, we carry out the bounding operation using a parametric right-hand-side simplex algorithm.

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